Testing arrangements of the above type are well known. In general, they include a testing adapter or the like, which is equipped with a multitude of resilient contact pins adapted for contacting the printed circuit board or similar items to be tested. In this context, reference may be made, for instance, to an article by Kruger entitled "Pruefmittel zur Pruefung von Leiter platten fuer Uhren", appearing in the Jahrbuch der Deutschen Gesellschaft fuer Chronometrie, Vol. 30, 1979, pp. 269-276. Especially on page 272, FIG. 3, there is disclosed the construction of resilient contact pins of the type here under consideration. These resilient contact pins are inserted either directly into bores of the testing adapter, or in sleeves which are, in turn, supported in respective bores of the testing adapter. The assembly of such known resilient contact pins was accomplished heretofore in such manner that a spring and a contact member are introduced into the interior of a hollow cylinder member, and then an abutment is formed on the member for determining the frontmost or extended position of the contact member relative to the cylinder member into which a spring accommodated in the cylinder member can press a piston of the contact member. This abutment is formed by an inward swaging of the upper end of the cylinder member or by an inward pressing of an internal annular bulge into the cylinder member. However, such deformations of the cylinder member to form the abutment for the piston of the contact member are difficult to accomplish, because of the extremely small diameter of the cylinder member which amounts in general at most to 2.5 millimeters and usually even to considerably less. Moreover, this subsequent deformation brings about the danger of damage to the cylinder member, especially at the internal sliding surface thereof which serves to slidingly guide the piston of the contact pin. Such damages may result, in the worst case, in the contact pin becoming unusable, or in the best case in a situation where the piston of the contact member will be at least occasionally jammed.